Sine and cosine integrals on non-uniform grid

Calculates integrals f(x)*sin(k*x)*dx and f(x)*cos(k*x)*dx with high precision for any value of k

Description

See the comments given inside the *.m files. Can be used for a Fourier transform on a non-uniform grid.

• MATLAB release: MATLAB 7.1.0 (R14SP3)

[T. U.]

 

[Bochore Guchuma]

This one is a nice approach.
I have a problem of integrating mixed harmonic signals of different orders,such as integral of f(wt)=cos(wt)+sin(2*wt)+sin(7*wt) and the like.
I have tried using iterative numerical method as well as with cumtrapz method. But since a cosine signal has a value of 1 at t=0,it was difficult for me to find the initial condition for a mixed signal of different harmonic combinations!
Any help I would appreciate.
Regards,

[John D'Errico]

Shaun's assessment is closely in line with mine. The help is reasonable. I'm vaguely uncomfortable with the choice of method, although a valid assessment of the method used here would force me to do a complete re-write and in-depth analysis.

For example, I'm unhappy with use of a continuous but not differentiable piecewise quadratic to approximate the function. A cubic spline would have been a very simple alternative here.

I'm also a bit worried about how the author handles large values of k*x, and I don't see why the author has chosen to use a high order Taylor series expansion when the integral is available directly.

Finally, there is a lot of unnecessarily cloned and loopy code.

You may or may not be happy with this code. Like Shaun, I can't come up with a rating that fits it.

[Shaun S]

Since I don't have time to really rate this file, I will just make a couple comments. It is loopy, certain areas could be vectorized. I am not sure the user would want a second order polynomial approximating, say, a square wave. Using Taylor Expansion? Even for an analytical result, there are better ways to proceed on a sine function. Again, I did not spend too much time.